Pseudorandom functions are not to be confused with pseudorandom generators (PRGs). The guarantee of a PRG is that a single output appears random if the input was chosen at random. On the other hand, the guarantee of a PRF is that all its outputs appear random, regardless of how the corresponding inputs were chosen, as long as the function was drawn at random from the PRF family.

A pseudorandom function family can be constructed from any pseudorandom generator, using, for example, the construction given by Goldreich, Goldwasser, and Micali.[1]

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A PRF is an efficient (i.e. computable in polynomial time) deterministic function that maps two distinct sets (domain and range).

Essentially a true random function would just be composed of a look-up table filled with random entries. However, in practice a PRF has only one input d (domain) and a hidden random seed (range) which when run multiple times with the same input, always outputs the same value. Nonetheless, given an arbitrary input the output looks random due to the random seed.

A PRF is considered to be good if its behavior is indistinguishable from a true random function. Therefore, given a true random function and a PRF, there should be no efficient method of determining if the output was produced by a true random function or the PRF.

In an oblivious pseudorandom function, information is concealed from two parties that are involved in a PRF.[2] That is, if Alice gives the input for a pseudorandom function to Bob, and Bob computes a PRF and gives the output to Alice, Bob is not able to see either the input or the output, and Alice is not able to see the secret key Bob uses with the pseudorandom function. This enables transactions of sensitive cryptographic information to be secure even between untrusted parties.